Comparison and Rigidity Theorems in Semi-Riemannian Geometry

The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian case correspond to one-sided bounds on the sectional curvatures. Starting from 2-dimensional rigidity results and using an inductive technique, a new class of gap-type rigidity theorems is proved for semi-Riemannian manifolds of arbitrary index, generalizing those first given by Gromov and Greene-Wu. As applications we prove rigidity results for semi-Riemannian manifolds with simply connected ends of constant curvature.Comment: 46 pages, amsart, to appear in Comm. Anal. Geo

A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for $C^0$ spacelike hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped product splitting theorem is given.Comment: 37 pages, 1 figure, ams-latex using eepi

Sauromalus hispidus

Number of Pages: 4Integrative BiologyGeological Science

Human factors in space telepresence

The problems of interfacing a human with a teleoperation system, for work in space are discussed. Much of the information presented here is the result of experience gained by the M.I.T. Space Systems Laboratory during the past two years of work on the ARAMIS (Automation, Robotics, and Machine Intelligence Systems) project. Many factors impact the design of the man-machine interface for a teleoperator. The effects of each are described in turn. An annotated bibliography gives the key references that were used. No conclusions are presented as a best design, since much depends on the particular application desired, and the relevant technology is swiftly changing

The sun's magnetic sector structure

The synoptic appearance of solar magnetic sectors is studied using 454 sector boundaries observed at earth during 1959-1973. The sectors are clearly visible in the photospheric magnetic field. Sector boundaries can be clearly identified as north-south running demarcation lines between regions of persistent magnetic polarity imbalances. These regions extend up to about 35 deg of latitude on both sides of the equator. They generally do not extend into the polar caps. The polar cap boundary can be identified as an east-west demarcation line marking the poleward limit of the sectors. The typical flux imbalance for a magnetic sector is about 4 x 10 to the 21st power Maxwells

Subcritical water and carbonated water extraction of anthocyanins from grape pomace

Grape pomace, a by-product of juice and wine processing, is a rich source of anthocyanins, antioxidant compounds that may afford protection against cancer and coronary heart disease. Unfortunately, traditional extraction of these antioxidants involves use of organic solvents, which pose serious safety and disposal problems for industry. Clearly a need exists for “green” extraction technologies—such as use of subcritical water—that eliminate or reduce the amount of organic solvents. In this study, we determined the efficacy of subcritical and carbonated water in extraction of anthocyanins from red grape pomace. Extraction variables including particle size, pomace mass, and temperature were optimized, and results were compared with those obtained using a traditional solvent-extraction method. According to the total anthocyanin assay, optimum conditions for extraction consisted of the smaller particle size (400 µm) and temperature of 100°C. Under these conditions, subcritical water and carbonated water extracted about 70% of anthocyanins obtained using the traditional organic solvent method. The highest antioxidant-capacity value measured by the ORAC assay was obtained at 140°C, suggesting that Maillard browning products were produced when grape pomace was exposed to increasing temperatures. Subcritical water appears to be a promising, environmentally benign technology to recover health-promoting compounds from grape-processing waste

Generation of mechanical interference fringes by multi-photon counting

Exploring the quantum behaviour of macroscopic objects provides an intriguing avenue to study the foundations of physics and to develop a suite of quantum-enhanced technologies. One prominent path of study is provided by quantum optomechanics which utilizes the tools of quantum optics to control the motion of macroscopic mechanical resonators. Despite excellent recent progress, the preparation of mechanical quantum superposition states remains outstanding due to weak coupling and thermal decoherence. Here we present a novel optomechanical scheme that significantly relaxes these requirements allowing the preparation of quantum superposition states of motion of a mechanical resonator by exploiting the nonlinearity of multi-photon quantum measurements. Our method is capable of generating non-classical mechanical states without the need for strong single photon coupling, is resilient against optical loss, and offers more favourable scaling against initial mechanical thermal occupation than existing schemes. Moreover, our approach allows the generation of larger superposition states by projecting the optical field onto NOON states. We experimentally demonstrate this multi-photon-counting technique on a mechanical thermal state in the classical limit and observe interference fringes in the mechanical position distribution that show phase superresolution. This opens a feasible route to explore and exploit quantum phenomena at a macroscopic scale.Comment: 16 pages, 4 figures. v1: submitted for review on 28 Jan 2016. v2: significantly revised manuscript. v3: some further revisions and some extra results included. v3: new results added, extra author added, close to published version, supplementary material available with published versio

The investigation of vertebral injury sustained during aircrew ejection. Phase 2a - Basic science experimental design and investigation of dynamic characteristics of vertebral columns considered as an engineering structure Annual report, 1 Nov. 1966 - 31 Oct. 1967

Dynamic strength studies on human vertebrae for correlation with data on effects of forcible ejection from disabled aircraf

Hubble Space Telescope Imaging and Spectroscopy of the Sirius-Like Triple Star System HD 217411

We present Hubble Space Telescope imaging and spectroscopy of HD 217411, a G3 V star associated with the extreme ultraviolet excess source (EUV 2RE J2300-07.0). This star is revealed to be a triple system with a G 3V primary (HD 217411 A) separated by ~1.1" from a secondary that is in turn composed of an unresolved K0 V star (HD 217411 Ba) and a hot DA white dwarf (HD 217411 Bb). The hot white dwarf dominates the UV flux of the system. However; it is in turn dominated by the K0 V component beyond 3000 {\AA}. A revised distance of 143 pc is estimated for the system. A low level photometric modulation having a period of 0.61 days has also been observed in this system along with a rotational velocity on the order of 60 km s-1 in the K0 V star. Together both observations point to a possible wind induced spin up of the K0 V star during the AGB phase of the white dwarf. The nature of all three components is discussed as are constraints on the orbits, system age and evolution.Comment: 11 pages, 6 figure